Recall that finitely generated modules are Tor-rigid over regular local rings [1]}, [2]}.
Set \(\operatorname{\mathcal {Z}}:=\operatorname{Spec}(R)\setminus \lbrace 0\rbrace \) . By Proposition REF , \(\Gamma _{\operatorname{\mathcal {Z}}}(L)=L)\)  for every \(L\in \operatorname{mod}(R)\) . Now the assertion follows from Lemma REF (a), (b) and Proposition REF .
